Showing papers by "Choy Heng Lai published in 2000"
Posted Content•
TL;DR: In this paper, the authors proposed a method to extract messages masked by a chaotic signal of a time-delay system with very high dimension and many positive Lyapunov exponents using a special embedding coordinate.
Abstract: We show how to extract messages masked by a chaotic signal of a time-delay system with very high dimension and many positive Lyapunov exponents. Using a special embedding coordinate, the infinite dimensional phase space of the time-delay system is projected to a special three-dimensional space, which enables us to identify the time-delay of the system from the transmitted signal, and reconstruct the chaotic dynamics to unmask the hidden message successfully. The message extraction procedure is illustrated by simulations with Mackey-Glass time-delay system for two type of masking schemes and different kinds of messages.
116 citations
TL;DR: The synchronization of two different chaotic oscillators is studied, based on an open-loop control – the entrainment control, and a hierarchical idea to synchronize multiple chaotic subsystems is proposed.
Abstract: The synchronization of two different chaotic oscillators is studied, based on an open-loop control – the entrainment control. We consider two types of synchronization: complete synchronization and effectively complete synchronization. The sufficient conditions that two different systems can be synchronized by this method is discussed. Furthermore, a hierarchical idea to synchronize multiple chaotic subsystems is proposed.
41 citations
TL;DR: In this article, the authors analyzed the behavior of synchronization with positive conditional Lyapunov exponents in computer simulations of the synchronization of chaotic systems with various couplings, and demonstrate that synchronization is an outcome of finite precision in numerical simulations.
26 citations
TL;DR: In this article, an entirely data-based method to detect chaos from the time series is developed by introducing p -neighbour points (the p -steps-neighbor points).
Abstract: In this paper, an entirely data-based method to detect chaos from the time series is developed by introducing p -neighbour points (the p -steps -neighbour points). We demonstrate that for deterministic chaotic systems, there exists a linear relationship between the logarithm of the average number of p -neighbour points, lnn p , , and the time step, p . The coefficient can be related to the KS entropy of the system. The effects of the embedding dimension and noise are also discussed.
3 citations
Posted Content•
TL;DR: In this paper, the synchronization with positive conditional Lyapunov was shown to be a combined result of the contracting region of the chaotic system and the finite precision in computer simulations.
Abstract: Synchronization of chaotic system may occur only when the largest conditional Lyapunov exponent of the driven system is negative. The synchronization with positive conditional Lyapunov reported in a recent paper (Phys. Rev. E, {\bf 56}, 2272 (1997)) is a combined result of the contracting region of the system and the finite precision in computer simulations.
1 citations
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TL;DR: In this paper, a class of nonlinear dynamical systems possessing an invariant subspace can display interesting dynamical behavior, such as on-off intermittency and bubbling.
Abstract: Nonlinear dynamical systems possessing an invariant subspace can display interesting dynamical behavior, such as on-off intermittency and bubbling. This letter shows that a class of such systems have amazing features of (1) supersensitivity to small input signals and (2) robustness of the supersensitivity in the presence of noise. These features make the systems very promising as small signal detectors.
Posted Content•
TL;DR: This paper considers the use of parameter adaptive control techniques to extract the message, based on the assumptions that the authors know the equation form of the chaotic system in the transmitter but do not have access to the precise values of the parameters which are kept secret as a secure set.
Abstract: It has been proposed to realize secure communication using chaotic synchronization via transmission of binary message encoded by parameter modulation in the chaotic system. This paper considers the use of parameter adaptive control techniques to extract the message, based on the assumptions that we know the equation form of the chaotic system in the transmitter but do not have access to the precise values of the parameters which are kept secret as a secure set. In the case that a synchronizing system can be constructed using parameter adaptive control by the transmitted signal and the synchronization is robust to parameter mismatches, the parameter modulation can be revealed and the message decoded without resorting to exact parameter values in the secure set. A practical local Lyapunov function method for designing parameter adaptive control rules based on originally synchronized systems is presented.